The propagation of high-frequency (HF) signals over long distances by way of ionospheric channels is studied by computing ray trajectories in numerically specified ionospheres without magnetic field. Horizontal ionization gradients are introduced to provide favorable conditions for the injection of rays from the ground into elevated ionospheric ducts. Electron density height distributions with and without ionization valleys are considered. The ducting efficiency, expressed in terms of frequency-and launch-elevation-angle interval for trapped rays, is controlled by negative horizontal ionization gradients for successful injection of rays and by the shape of the electron density height profile and its change with distance. Long-range ionospheric ducting of HF rays does not require but is facilitated by the continued presence of an ionization valley in the plane of the ray trajectory.
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